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Mathematics Curriculum Supplement Geometry (G-CO.C.10) Geometry Mathematics Highly-Leveraged Standard1 G-CO.C.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. Student Learning Targets: Students will be able to: classify triangles by their sides and angles. identify two parallel lines, the midpoint of a segment, the base and base angles of isosceles triangles, and the midsegments of a triangle. prove and apply the triangle sum theorem and the exterior angle theorem. prove and apply the idea that the base angles (and two sides) of an isosceles triangle are congruent (and the converse). prove an equilateral triangle is equiangular (and the converse). prove and apply the idea that the segment joining midpoints of two sides of a triangle are parallel to the third side and half the length. prove the medians of a triangle meet at the centroid. prove the perpendicular bisectors of a triangle meet at the circumcenter. prove the altitudes of a triangle meet at the orthocenter. prove the angle bisectors of a triangle meet at the incenter. Performance Level Descriptors Standard Minimally Proficient Partially Proficient Proficient Highly Proficient The Minimally The Partially Proficient The Proficient student The Highly Proficient Proficient student student student Congruence G-CO.C Describes examples of Determines the validity Proves theorems about Applies theorems about [10] theorems about of statements within a triangles. (Theorems triangles to a real-life triangles. given proof of a theorem include: measures of context. about triangles. interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.) 1 Highly-Leveraged Standards are the most essential for students to learn because they have endurance, leverage and essentiality. This definition for highly-leveraged standards was adapted from the website of Millis Public Schools, K-12, in Massachusetts, USA. http://www.millis.k12.ma.us/services/curriculum_assessment/brochures Specifically for mathematics, the Highly-Leveraged Standards are the Major Content/Clusters as defined by the AZCCRS Grade Level Focus documents. They should encompass a range of at least 65%-75% for Major Content/Clusters and a range of 25%-35% for Supporting Cluster Instruction. See the Grade Level Focus documents at: https://cms.azed.gov/home/GetDocumentFile?id=57069f7baadebe0bccd0a8b5 TUSD Department of Curriculum and Instruction Curriculum 3.0 Revised 4/30/2017 4:50 PM Page 1